Vocabulary
What is a rigid transformation?
A transformation that preserves size & shape.
Translate point A(–2, 4) by the rule (x, y) →
(x + 3, y – 2). What is A′?
(1, 2)
Reflect point (4, –2) across the y-axis. What is the new point?
(–4, –2)
A point is translated 2 units right, then 2 units left. Where does it end up?
Back at start.
What does it mean for two figures to be congruent?
Same shape and size.
Name the three types of rigid transformations.
Translation, reflection, rotation.
Translate triangle with vertices (1,1), (2,3), (3,1) 4 units right. List new coordinates.
(5,1), (6,3), (7,1)
Rotate point (0, 5) 180° about the origin. What is the new point?
(0, –5)
A figure is reflected across the y-axis, then across the x-axis. What transformation does this equal?
180° rotation about the origin.
True or False: If two figures can be mapped onto each other using rigid transformations, they are congruent.
True.
True or False: Dilations are rigid transformations.
False, surprise that is your next unit;)
A square with side length 2 units is translated 5 units up. What happens to its area?
Area stays the same.
Reflect triangle with vertices (1,1), (2,2), (3,1) across the x-axis. List new coordinates.
(1, –1), (2, –2), (3, –1)
A square is rotated 90° counterclockwise, then translated up 3 units. How is its size affected?
Size unchanged.
Two triangles are congruent. One has sides 3, 4, 5. What are the side lengths of the other triangle?
3, 4, 5.
Define congruent figures
Figures with same shape & size.
Write a Sequence of transformations that moves point P(–5, 0) to P′(2, 7).
(x + 7, y + 7)
Rotate point (–3, 2) 90° clockwise about the origin.
(2, 3)
A triangle at (1,2), (2,4), (3,2) is reflected over the y-axis and then translated 1 unit down. Write its new coordinates.
(–1,1), (–2,3), (–3,1)
A triangle has vertices at (0,0), (2,0), (1,3). Another triangle has vertices (–2,0), (0,0), (–1,3). Describe the transformation(s) that prove the triangles are congruent.
Reflection across y-axis.
Explain the difference between a rigid transformation and a non-rigid transformation.
Rigid = preserves size; non-rigid (dilation) = changes size.
A figure is translated left 2 and up 3. Describe this movement using a coordinate rule.
(x – 2, y + 3)
A figure is reflected over the x-axis and then rotated 180° about the origin. Describe how its orientation changes.
Flipped and rotated, orientation changes but size/shape preserved.
Describe a sequence of transformations that maps a figure onto itself. Give an example.
A 360° rotation or reflection across both axes
Explain why all rigid transformations preserve congruence. Give an example using coordinates.
They preserve distance and angle measures